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  <meta name="description" content="前言道格拉斯-普克算法 (Douglas–Peucker algorithm，亦称为拉默-道格拉斯-普克算法、迭代适应点算法、分裂与合并算法)是将曲线近似表示为一系列点，并减少点的数量的一种算法。它的优点是具有平移和旋转不变性，给定曲线与阈值后，抽样结果一定。因为网上关于道格拉斯普克算法的讲解很多，主要是使用递归实现的，这里就不赘述了。">
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          <h1 class="post-title" itemprop="name headline">GIS算法基础（九）矢量压缩算法-道格拉斯普克算法

            
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              <time title="创建时间：2019-06-01 13:42:05" itemprop="dateCreated datePublished" datetime="2019-06-01T13:42:05+08:00">2019-06-01</time>
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        <h1 id="前言"><a href="#前言" class="headerlink" title="前言"></a>前言</h1><p>道格拉斯-普克算法 (Douglas–Peucker algorithm，亦称为拉默-道格拉斯-普克算法、迭代适应点算法、分裂与合并算法)是将曲线近似表示为一系列点，并减少点的数量的一种<a href="https://baike.baidu.com/item/算法/209025" target="_blank" rel="noopener">算法</a>。它的优点是具有平移和旋转不变性，给定曲线与阈值后，抽样结果一定。</p><p>因为网上关于道格拉斯普克算法的讲解很多，主要是使用递归实现的，这里就不赘述了。</p><a id="more"></a>

<p><strong>远程仓库地址：</strong></p>
<p><strong><a href="https://github.com/XiaoZhong233/GIS_ALG" target="_blank" rel="noopener">https://github.com/XiaoZhong233/GIS_ALG</a></strong></p>
<hr>
<p>直接上代码和演示</p>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">//概化折线 道格拉斯普克算法</span></span><br><span class="line"><span class="comment">/**</span></span><br><span class="line"><span class="comment"> * 根据中间点到首尾点的连线的距离与阈值的关系判断是否保留某点</span></span><br><span class="line"><span class="comment"> * <span class="doctag">@param</span> threshold 阈值越小，保留的点越多，抽稀程度低；阈值越大，删除的点越多，抽稀程度高</span></span><br><span class="line"><span class="comment"> * <span class="doctag">@return</span></span></span><br><span class="line"><span class="comment"> */</span></span><br><span class="line"><span class="function"><span class="keyword">public</span> Polyline <span class="title">simplify_Douglas_Peucker</span><span class="params">(<span class="keyword">double</span> threshold)</span> </span>&#123;</span><br><span class="line">	<span class="comment">//初始化</span></span><br><span class="line">	<span class="keyword">for</span>(Point point:<span class="keyword">this</span>.getPoints()) &#123;</span><br><span class="line">		point.setEnable(<span class="keyword">true</span>);</span><br><span class="line">	&#125;</span><br><span class="line">	List&lt;Point&gt; selectedPoints = <span class="keyword">new</span> ArrayList&lt;&gt;();</span><br><span class="line">	Collections.addAll(selectedPoints,  <span class="keyword">new</span>  Point[<span class="keyword">this</span>.points.size()]); </span><br><span class="line">	Collections.copy(selectedPoints, <span class="keyword">this</span>.points);</span><br><span class="line">	simplify(selectedPoints, threshold);</span><br><span class="line">	<span class="comment">//标记了删除的点，全部删掉</span></span><br><span class="line">	Iterator&lt;Point&gt; iterator = selectedPoints.iterator();</span><br><span class="line">	<span class="keyword">while</span> (iterator.hasNext()) &#123;</span><br><span class="line">		Point point = (Point) iterator.next();</span><br><span class="line">		<span class="keyword">if</span>(!point.isEnable()) &#123;</span><br><span class="line">			iterator.remove();</span><br><span class="line">		&#125;</span><br><span class="line">	&#125;</span><br><span class="line">	<span class="keyword">if</span>(debug) &#123;</span><br><span class="line">		System.out.println(<span class="string">"最后保留的点："</span>);</span><br><span class="line">		<span class="keyword">for</span>(Point p:selectedPoints) &#123;</span><br><span class="line">			System.out.println(p.toString());</span><br><span class="line">		&#125;</span><br><span class="line">	&#125;</span><br><span class="line">	<span class="comment">//恢复</span></span><br><span class="line">	<span class="keyword">for</span>(Point point:<span class="keyword">this</span>.getPoints()) &#123;</span><br><span class="line">		point.setEnable(<span class="keyword">true</span>);</span><br><span class="line">	&#125;</span><br><span class="line">	</span><br><span class="line">	<span class="keyword">return</span> <span class="keyword">new</span> Polyline(selectedPoints);</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

<p><img src="" alt="点击并拖拽以移动"></p>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br><span class="line">75</span><br><span class="line">76</span><br><span class="line">77</span><br><span class="line">78</span><br><span class="line">79</span><br><span class="line">80</span><br><span class="line">81</span><br><span class="line">82</span><br><span class="line">83</span><br><span class="line">84</span><br><span class="line">85</span><br><span class="line">86</span><br><span class="line">87</span><br><span class="line">88</span><br><span class="line">89</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">/**</span></span><br><span class="line"><span class="comment"> * </span></span><br><span class="line"><span class="comment"> * <span class="doctag">@param</span> polyline 折线</span></span><br><span class="line"><span class="comment"> * <span class="doctag">@param</span> threshold 阈值越小，保留的点越多，抽稀程度低；阈值越大，删除的点越多，抽稀程度高</span></span><br><span class="line"><span class="comment"> * <span class="doctag">@return</span></span></span><br><span class="line"><span class="comment"> */</span></span><br><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> Polyline <span class="title">simplify_Douglas_Peucker</span><span class="params">(Polyline polyline,<span class="keyword">double</span> threshold)</span> </span>&#123;</span><br><span class="line">	<span class="keyword">return</span> polyline.simplify_Douglas_Peucker(threshold);</span><br><span class="line">&#125;</span><br><span class="line"></span><br><span class="line"><span class="comment">//抽稀点</span></span><br><span class="line"><span class="function"><span class="keyword">private</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title">simplify</span><span class="params">(List&lt;Point&gt; points,<span class="keyword">double</span> threshold)</span> </span>&#123;</span><br><span class="line">	<span class="comment">//threshold = Math.abs(threshold);</span></span><br><span class="line">	<span class="keyword">if</span>(points.size()&lt;<span class="number">3</span>) &#123;</span><br><span class="line">		<span class="keyword">return</span>;</span><br><span class="line">	&#125;</span><br><span class="line">	Line line = <span class="keyword">new</span> Line(points.get(<span class="number">0</span>),points.get(points.size()-<span class="number">1</span>));</span><br><span class="line">	Point maxPoint = <span class="keyword">null</span>;</span><br><span class="line">	<span class="keyword">double</span> maxDis = <span class="number">0</span>;</span><br><span class="line">	<span class="comment">//System.out.println(points.size());</span></span><br><span class="line">	<span class="keyword">for</span>(Point point:points) &#123;</span><br><span class="line">		<span class="keyword">double</span> dis =  line.getDistancefromPoint(point);</span><br><span class="line">		<span class="keyword">if</span>(debug) &#123;</span><br><span class="line">			System.out.println(point.toString());</span><br><span class="line">		&#125;</span><br><span class="line">		<span class="comment">//System.out.println(dis);</span></span><br><span class="line">		<span class="keyword">if</span>(Double.doubleToLongBits(dis)&gt;Double.doubleToLongBits(maxDis) &amp;&amp; line.getStart()!=point &amp;&amp; line.getEnd()!=point) &#123;</span><br><span class="line">			maxDis = dis;</span><br><span class="line">			maxPoint = point;</span><br><span class="line">		&#125;</span><br><span class="line">		</span><br><span class="line">	&#125;</span><br><span class="line">	<span class="keyword">if</span>(debug) &#123;</span><br><span class="line">		System.out.println(<span class="string">"max:"</span>+maxDis);</span><br><span class="line">		System.out.println(<span class="string">"阈值:"</span>+threshold);</span><br><span class="line">		System.out.println(<span class="string">"保留最大点与首尾点"</span>);</span><br><span class="line">	&#125;</span><br><span class="line">	<span class="comment">//保留最大点与首尾点</span></span><br><span class="line">	<span class="keyword">if</span>(maxDis&gt;threshold &amp;&amp; maxPoint!=<span class="keyword">null</span>) &#123;</span><br><span class="line">		<span class="keyword">if</span>(debug) &#123;</span><br><span class="line">			System.out.println(<span class="string">"最大点:"</span>+maxPoint.toString());</span><br><span class="line">		&#125;</span><br><span class="line">		</span><br><span class="line">		<span class="comment">//涉及到删除元素不可以用for或while循环，因为会改变元素的位置</span></span><br><span class="line">		Iterator&lt;Point&gt; iterator = points.iterator();</span><br><span class="line">		<span class="keyword">while</span> (iterator.hasNext()) &#123;</span><br><span class="line">			Point p = (Point) iterator.next();</span><br><span class="line">			<span class="keyword">if</span>(!(p==line.getStart()||p==line.getEnd()||p==maxPoint)) &#123;</span><br><span class="line">				<span class="comment">//标记不可用，这里指删除</span></span><br><span class="line">				<span class="comment">//因为还需要留着左右部分的点做进一步的简化，不可以在这里进行删除操作 防止被gc掉</span></span><br><span class="line">				p.setEnable(<span class="keyword">false</span>);</span><br><span class="line">				<span class="keyword">if</span>(debug) &#123;</span><br><span class="line">					System.out.println(<span class="string">"删除的点："</span>+p.toString());</span><br><span class="line">				&#125;</span><br><span class="line">			&#125;<span class="keyword">else</span> &#123;</span><br><span class="line">				p.setEnable(<span class="keyword">true</span>);</span><br><span class="line">				<span class="keyword">if</span>(debug) &#123;</span><br><span class="line">					System.out.println(<span class="string">"保留的点："</span>+p.toString());</span><br><span class="line">				&#125;</span><br><span class="line">			&#125;</span><br><span class="line">		&#125;</span><br><span class="line">		<span class="comment">//以maxPoint把折线分为两部分接着简化</span></span><br><span class="line">		List&lt;Point&gt; leftPart = points.subList(<span class="number">0</span>, points.indexOf(maxPoint)+<span class="number">1</span>);</span><br><span class="line">		List&lt;Point&gt; rightPart = points.subList(points.indexOf(maxPoint), points.size());</span><br><span class="line">		<span class="keyword">if</span>(debug) &#123;</span><br><span class="line">			System.out.println(String.format(<span class="string">"left [1]-[%d]"</span>, points.indexOf(maxPoint)+<span class="number">1</span>));</span><br><span class="line">			System.out.println(String.format(<span class="string">"right [%d]-[%d]"</span>, points.indexOf(maxPoint)+<span class="number">1</span>, points.size()));</span><br><span class="line">		&#125;</span><br><span class="line">		simplify(leftPart, threshold);</span><br><span class="line">		simplify(rightPart, threshold);</span><br><span class="line">	<span class="comment">//只保留首尾点</span></span><br><span class="line">	&#125;<span class="keyword">else</span> &#123;</span><br><span class="line">		Iterator&lt;Point&gt; iterator = points.iterator();</span><br><span class="line">		<span class="keyword">while</span> (iterator.hasNext()) &#123;</span><br><span class="line">			Point p = (Point) iterator.next();</span><br><span class="line">			<span class="keyword">if</span>(!(p.equals(line.getStart())||p.equals(line.getEnd()))) &#123;</span><br><span class="line">				p.setEnable(<span class="keyword">false</span>);</span><br><span class="line">				<span class="keyword">if</span>(debug) &#123;</span><br><span class="line">					System.out.println(<span class="string">"删除的非首尾点："</span>+p.toString());</span><br><span class="line">				&#125;</span><br><span class="line">			&#125;<span class="keyword">else</span> &#123;</span><br><span class="line">				<span class="keyword">if</span>(debug) &#123;</span><br><span class="line">					System.out.println(<span class="string">"保留的首尾点："</span>+p.toString());</span><br><span class="line">				&#125;</span><br><span class="line">				p.setEnable(<span class="keyword">true</span>);</span><br><span class="line">			&#125;</span><br><span class="line">		&#125;</span><br><span class="line">	&#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

<p><img src="" alt="点击并拖拽以移动"></p>
<h1 id="结果："><a href="#结果：" class="headerlink" title="结果："></a>结果：</h1><p>原始图像：</p>
<p><img src="https://zhong-blog.oss-cn-shenzhen.aliyuncs.com/blog/20190907205911.png!blog" alt="20190907205911"><img src="" alt="点击并拖拽以移动"></p>
<p>道格拉斯普克算法概化 阈值 130：</p>
<p><img src="https://zhong-blog.oss-cn-shenzhen.aliyuncs.com/blog/20190907205921.png!blog" alt="20190907205921"><img src="" alt="点击并拖拽以移动"></p>
<p>道格拉斯普克算法概化 阈值 180：</p>
<p><img src="https://zhong-blog.oss-cn-shenzhen.aliyuncs.com/blog/20190907205933.png!blog" alt="20190907205933"><img src="" alt="点击并拖拽以移动"></p>
<p>道格拉斯普克算法概化 阈值  250：</p>
<p><img src="https://zhong-blog.oss-cn-shenzhen.aliyuncs.com/blog/20190907205945.png!blog" alt="20190907205945"><img src="" alt="点击并拖拽以移动"></p>
<p>控制台打印：</p>
<p><img src="https://zhong-blog.oss-cn-shenzhen.aliyuncs.com/blog/20190907205955.png!blog" alt="20190907205955"><img src="" alt="点击并拖拽以移动"></p>

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